The FBF is a well know "meme" on 4chans /b/ random board, it is a picture of a bullfrogs head with a green pattern background, people add text on a website called meme generator that is agreeable and adheres to "foul bachelor behavior". This is one of the most popular memes on the /b/ board as many people who frequent /b/ can relate to it.

The text that people put on the picture is usually in a simple "event" - "reaction" context (see examples)

The text, when done properly usually contains a common, normally undesirable character trait being expressed, such as wearing dirty clothing, "fapping" (masturbating) into a sock, wearing a fapped into sock, microwaving a harddrive out of paranoia, not caring about surroundings, being disoriented about what time it is after an unexpected nap, etc. etc.

(Top) See picture of rotting dick on /b/

(Bottom) Fap 2 minutes later

(Top) Clothing worn once on the floor
(Bottom) Floordrobe

(Top) Wake up, see 2:00 on the clock
(Bottom) Look out window to see if AM or PM

2) A person that you are friendly with and/or think is cool but don't necessarily hang out or know.

a. Co-worker: "Don't worry we're FBFs so I'm sure we'll keep in touch after I leave."
b. New acquaintance: "Hey, it was really good meeting/you hanging out last night. Let's be FBFs and get together soon."
c. You: "I wouldn't say were like friend-friends...we're just FBFs."